While group Administrators can access all of the functionality on the group's Profile, Messages and Calendar, a group Coach cannot:
Change the group's name, description, visibility or institutional settings
Add/remove people from the group
Assign/revoke coach or admin roles for others
Delete posts
Pin/Unpin posts
In this way, the coach role is intended to be used by those who need to administer the Calendar only, and not the group as a whole.